Agriculture Reference
In-Depth Information
Panel A
Panel C
Panel B
Farmer's effort ( e
Variable input ( k
Land attributes ( l
h
h
h
e
l
k
h
h
h
e
k
l
A
s*
h
e
s*
h
k
s*
h
l
C
B
c
r
w
q*c
D
r
s
s
e
e*
e
k
l*
l
l
k*
Note:
s
* is chosen so that
AB
=
CD
.
Figure 5.1
Output shares and input use:
q
∗
=
s
∗
implies
k
q
=
0. Thus, if inputs are not shared, the optimal sharing rules must satisfy
e
s
(h
e
−
w)
+
l
s
(h
l
−
r)
+
k
s
(h
k
−
c)
=
0,
and
(5.7)
q
∗
=
1.
(5.8)
The optimal use of inputs is illustrated by figure 5.2, which considers the case where the
farmer pays all of the input costs. For
e
l
, the incentives for input use are the same as
when the inputs are shared, resulting in the marginal distortions AB and CD. For each of
the other
and
inputs, however, the lack of input sharing results in lower use and a marginal
distortion equal to EF per input. The optimal output share
k
s
∗
is chosen so that the marginal
negative distortions (AB and EF) are exactly offset by the marginal positive distortion (CD);
that is, AB + EF = CD. If there are many
+
i
=
1
(
CD
.
This analysis indicates a dichotomy in the choice of the optimal input share: Either input
and output shares are equal, or the farmer pays the entire input cost. Under our assumptions,
an optimal cropshare contract has no middle ground:
(n)
other
k
inputs, then
AB
EF
)
=
q
∗
=
s
∗
or
q
∗
=
1.
PREDICTION 5.1 Parties to cropshare contracts will either (i) only share output, the pure
cropshare contract where
q
∗
=
s
∗
<
1 or (ii) share both inputs and output in the same
proportion, the input-output cropshare contract where
1, and
q
∗
=
s
∗
<
1.
Two more predictions immediately follow from this analysis.
